APPENDIX A 



OF THE COHESION OF FLUIDS, 



382. Theorem. If there be a series of 

 equal particles, arranged at equal intervals in 

 a right line, each attracting or repelling its 

 immediate neighbour, only with a constant 

 force/; the force FM, acting on any obstacle 

 M at one end of the whole line ^/, supposing 

 the other to be fixed, will be equal to/. 



The general principle of virtual velocities is XmS^s:=:0, 

 (/, 305) or, taking any one of the forces combined with each 

 other as the result of the rest, and in an opposite direc- 

 tion, MV^uzzlmSh: and in applying this principle, the 

 variations may be taken in any manner capable of repre- 

 senting their relations to each other, without confining 

 them to such as are likely to occur in the natural pheno- 

 mena to be considered ; and the motive force VM may 



always be found, if we can determine its equal — ^ . 



Now if the number of particles concerned be m, and their 



masses equal to unity, we shall have S«= — , since we may 



Tflr 



suppose the particles to remain equally distributed 

 throughout the line after the variation of their distances. 



